What is the equation of the line that passes through the point (-8, 3) and has a
slope of -1/4

Given parameters:

 Slope of the line  =

 Coordinates of the points = (-8, 3)

Unknown:

Equation of the line = ?

Solution:

To find the equation of the line, we must note that any straight line can be represented by the equation;

        y  = mx + c

 where x and y are the coordinates

             m is the slope

              c is the y-intercept of the line

Input the parameters and solve for c;

     x = -8 and y  = 3;

         3  = x (-8) + c

         3 = 2 + c

        c  = 1;

  So the equation of the line is ;

     y  = x + 1

     multiply through by 4;

   4y = -x + 4

The equation of the line is 4y = -x + 4

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).